2D Statistics - Linear Regression

Importing libraries

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
%config InlineBackend.figure_formats = ['svg']

Loading the data

df = pd.read_csv('weight-height.csv')
df.head(20)

	Gender	Height	Weight
0	Male	73.847017	241.893563
1	Male	68.781904	162.310473
2	Male	74.110105	212.740856
3	Male	71.730978	220.042470
4	Male	69.881796	206.349801
5	Male	67.253016	152.212156
6	Male	68.785081	183.927889
7	Male	68.348516	167.971110
8	Male	67.018950	175.929440
9	Male	63.456494	156.399676
10	Male	71.195382	186.604926
11	Male	71.640805	213.741169
12	Male	64.766329	167.127461
13	Male	69.283070	189.446181
14	Male	69.243732	186.434168
15	Male	67.645620	172.186930
16	Male	72.418317	196.028506
17	Male	63.974326	172.883470
18	Male	69.640060	185.983958
19	Male	67.936005	182.426648

Processing and printing the data

X= df['Height'].values*2.54 #inch to cm
Y = df['Weight'].values*0.453592 # pound to kg
plt.scatter(X,Y, s=10, color="blue", alpha=0.5)
plt.xlabel('Height')
plt.ylabel('Weight')
plt.show()

Covariance

N= X.shape[0]
Xm = X.mean()
Ym = Y.mean()
SumXY = X.dot(Y) #dot product ou produit scalaire
SEGxy= (SumXY/N)-Xm*Ym
print("N= ",N)
print('Xm= ', Xm)
print('Ym= ', Ym)
print("SumXY= ", SumXY)
print("COVxy= ",SEGxy)

N=  10000
Xm=  168.57360177724598
Ym=  73.22805433651739
SumXY=  124759253.78237706
COVxy=  131.60850759109417

Correlation Coefficient

SEGx = X.std()
SEGy = Y.std()
r = SEGxy/(SEGx*SEGy)
print('SEGx= ', SEGx)
print('SEGy= ', SEGy)
print('r= ', r)

SEGx=  9.772232778476152
SEGy=  14.563402841085871
r=  0.924756298740881

Linrear Regression

Regression line of Y on X: $y = ax + b$

a = SEGxy/(SEGx**2)
b = -a*Xm + Ym
print('a= ', a)
print('b= ',b)

a=  1.3781495809287396
b=  -159.0915843084424

plt.figure()
plt.scatter(X,Y, s=10, color="blue", alpha=0.5)
x= np.linspace(120, 210,1000)
y=a*x+b
plt.xlabel('Height')
plt.ylabel('Weight')
plt.plot(x,y,color='red')
plt.show()

Regression line of X on Y: $x = ay + b$

a2 = SEGxy/(SEGy**2)
b2 = -a2*Ym + Xm
print('a= ', a2)
print('b= ',b2)

a=  0.620523507676597
b=  123.13387264001777

plt.figure()
plt.scatter(Y,X, s=10, color="blue", alpha=0.5)
y2= np.linspace(25, 130,1000)
x2=a2*y2+b2
plt.ylabel('Height')
plt.xlabel('Weight')
plt.plot(y2,x2,color='red')
plt.show()